Normalization is important to effectively and correctly measure distance between vector representation. Here we propose three stages of normalization.
First, we use the intra-normalization [1]}, where the sum of residuals of each visual word \(v_i^j\)  is L2 normalized independently, where \(1 \le i \le K\)  and \(1 \le j \le M\) . This step is followed by inter-Z-score normalization across different visual words.
Given a vector \(X\) , its Z-score normalization is computed as: \(\frac{X-\mu }{\sigma }\) , where \(\mu \)  and \(\sigma \)  represent the mean and standard deviation of \(X\) . Let's denote the \(t^{th}\)  entry of \(V_i\)  as \(v_{i,t}\) , where \(V_i\)  is defined in Equation REF .
We apply the inter-Z-score normalization on each \( \left[ v_{1,t}, v_{2,t}, \ldots , v_{i,t}, \ldots , v_{K,t} \right]\) ,
where \(1 \le t \le {M \times d}\)  and \(1 \le i \le K \) .
At last, the gVLAD vector \(\mathcal {V}\)  is L2 normalized \(\mathcal {V} := \mathcal {V} / { \Vert  \mathcal {V}\Vert  }_2\) .
